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# Full text of "Analytical Mechanics"

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```MOTION OF A PARTICLE                       111
If Wi and W% denote the weights of two bodies of masses mi and m2, then by equation (X) we obtain
and                                      =      ,
m2     W\$
where g is the common acceleration due to gravitational attraction.
(2) If the forces acting upon the bodies are equal the masses are inversely proportional to the accelerations:
This gives us the second method by which masses may be compared. The following are more or less practicable applications of this method :
(a) Let A and B (Fig. 61) be two bodies connected with a long elastic string of negligible mass, placed on a perfectly
A
a           M
FIG. 61.
smooth and horizontal table. Suppose the string to be stretched by pulling A and B away from each other. It is evident that when the bodies are released they will be accelerated with respect to the table and that the accelerating force, that is, the pull of the string, will be the same for both bodies. Therefore if /i and /2 denote their accelerations at any instant of their motion, the ratio of their masses is given by the relation
(b) Suppose the bodies whose masses are to be compared```